In an earlier paper, partitions in which the smaller parts were required to appear at least k-times were considered. Some of those results were tied up with Rogers-Ramanujan type identities and mock theta functions. By considering more general conditions on initial parts we are led to natural explanations of many more identities contained in Slater’s compendium of 130 Rogers-Ramanujan identities.

The late Leon Ehrenpreis originally posed the problem of showing that the difference of the two Rogers-Ramanujan products had positive coefficients without invoking the Rogers-Ramanujan identities. We first solve the problem generalized to the partial products and subsequently solve several related problems. The object is to introduce the Anti-Telescoping Method which is capable of wide general...

New short and easy computer proofs of nite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the rst Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping.

Changing Concepts in Activity: Descriptive and Design Studies of Consequential Learning in Conceptual Practices Rogers Hall & A. Susan Jurow To cite this article: Rogers Hall & A. Susan Jurow (2015) Changing Concepts in Activity: Descriptive and Design Studies of Consequential Learning in Conceptual Practices, Educational Psychologist, 50:3, 173-189, DOI: 10.1080/00461520.2015.1075403 To link t...

a Department of Agricultural and Biological Engineering, University of Florida, 281 Frazier Rogers Hall, Gainesville, FL 32611-0570, USA b Dipartimento di Scienze Agrarie, Alma Mater Studiorum-Università di Bologna, Viale Giuseppe Fanin, 50, 40127 Bologna, Italy c Department of Agricultural and Biological Engineering, University of Florida, 287 Frazier Rogers Hall, Gainesville, FL 32611-0570, USA,